Abstract

This talk looks at the problem of decision under ambiguity from a computational perspective. We place the problem in the framework of composed optimization, where the objective function is computed in two steps. The first step associates a vector of first-level evaluations to a given decision, while the second step aggregates the entries of this vector into a single number. In this framework, it is often possible to define first-level evaluations in such a way that the problem of optimizing a weighted sum can be solved efficiently.

One may then profitably use a technique known as "iterative reweighting" to solve the optimization problem with more general forms of aggregation. This technique has already been used successfully in various fields, such as function approximation and optimal facility location. In the context of decision under ambiguity, the fixed point of the iteration can be viewed as providing a set of ambiguity-neutral probabilities associated with the ambiguity states. We give a novel interpretation of the fixed point as representing equilibrium in a population game. This allows the iterative reweighting method to be viewed as an evolutionary algorithm. We compute and compare the results of several different decision models, such as minmax regret, both under ambiguity in beliefs and under ambiguity in preferences. This is joint work with Anne Balter and Nikolaus Schweizer (both at Dept. of Econometrics and OR, Tilburg University).

Speaker